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Expanding Flow Maps

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling · 0 citations (OpenAlex)

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Introduces Expanding Flow Maps (EFMs) and Expanding Generative Flows (EFlows), enabling few-step generation where the state dimension or sequence length grows during inference, via an expand operator plus a transport map, for continuous conformers and discrete graphs and language.

Problem

Existing flow maps are restricted to fixed-dimensional continuous states or fixed-length discrete sequences, so they cannot generate outputs whose size is itself variable.

Approach

Factor the flow map between times into an expand operator that inserts noise-initialized coordinates (or tokens) and a transport map (mean velocity or mean denoiser) in the expanded space, formulated as a piecewise-deterministic Markov process with insertion jumps and a binomial/Poisson insertion head for discrete data.

Key results

• On GEOM-Drugs, EFlow with 20 steps reaches COV-R 81.78% and AMR-P 1.2672, competitive with multi-step diffusion baselines using 500-1000 steps; EFM+R with 14 steps gives the best GEOM-Drugs scores on all four metrics.
• On QM9 graph generation, EFM at 2 steps achieves FCD 0.40 versus CFM's 0.49, and at 1 step FCD 0.44 versus CFM's 2.14.
• On LM1B, EFlow at 1024 steps reaches generative perplexity 103.63 versus FLM's 111.36 at the same budget; EFM 1-step gives Gen. PPL 98.35 but with lower entropy 3.56.

Surprising findings

• Single-step EFM on language exhibits mode collapse, attributed to predicting full-length expansion and applying the flow map over the entire interval in one shot.
• EFlow without distillation on graphs already surpasses DeFoG at 100 steps and degrades more gracefully at 4 steps.

Limitations

• Empirical validation limited to at most 181-atom molecules and 128-length LM1B sequences; scaling to larger dimensionalities not explored due to compute.
• Entropy of generated language samples is lower than fixed-length baselines; single-step language sampling collapses.
• Only increasing-dimensionality interpolants considered; conditional noise is fixed Gaussian and insertion schedule is fixed.

Experimental setup

Datasets: GEOM-QM9 GEOM-Drugs QM9 LM1B

Benchmarks: GEOM-QM9 GEOM-Drugs QM9 LM1B

Metrics: COV-R AMR-R COV-P AMR-P validity uniqueness FCD generative perplexity entropy

Baselines: GeoDiff SubgDiff MSGEN ConfGF DeFoG CFM FLM Duo MDLM SDTT Di4C

Builds on: flow maps consistency models conditional flow matching DeFoG FLM

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